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Abstract

An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength λ to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50λ×50λ square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power). The diffraction efficiency and uniformity decrease as the size of the focused profile is reduced toward the diffraction limited spot size. These observations can be understood as a manifestation of the uncertainty principle.

Figures (5)

Optical setup of the beam shaping problem. The aperture represents the input pupil of the objective lens. The focal plane is divided into two regions. Ω represents the region of interest that contains and bounds the targeted beam shape. Its complement Ωc represents the remainder of the focal plane.

(A) Calculated irradiance distribution resulting when a circularly apodized flat-top input beam of radius R is passed through the phase-only DOE shown in Fig. 3 and focused using a 1.4-NA objective. The DOE was designed to reshape the beam into a flat-top square irradiance pattern of area 50λ×50λ (D=100λ). (B)–(D) Irradiances of the constituent x-, y-, and z-polarized components of the total field. Each profile is normalized to the peak of If.